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The McNemar test evaluates the hypothesis that two correlated proportion iscommon in $2 \times 2$ contingency tables with the same categories. This studydiscusses a test for symmetry in $2 \times 2$ contingency tables withnonignorable nonresponses. The proposed method is based on Takai and Kano(2008), which discusses a test for independence because a dependency assumptionbetween the two observed outcomes is required to obtain an identification.Here, we focus on three models and propose a test for symmetry in $2 \times 2$contingency tables with nonignorable nonresponses.

Test for symmetry in $2 \times 2$ contingency tables with nonignorable nonresponses